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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 6 — Mar. 21, 2005
  • pp: 2082–2088
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Two-mode photonic crystal fibers

Wei Jin, Zhi Wang, and Jian Ju  »View Author Affiliations


Optics Express, Vol. 13, Issue 6, pp. 2082-2088 (2005)
http://dx.doi.org/10.1364/OPEX.13.002082


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Abstract

Index-guiding photonic crystal fibers with appropriate structural parameters support the fundamental and second order modes over a practically infinite wavelength range. The polarization principal axes and mode field patterns of the modes can be made stable by having different size air-holes along the orthogonal directions. The potential applications of such two-mode PCFs are discussed.

© 2005 Optical Society of America

1. Introduction

An index-guiding photonic crystal fiber (PCF) has a solid core surrounded by a holey cladding region. A typical index-guiding PCF is fabricated by stacking silica capillaries periodically in a hexagonal close packed array and replacing the central capillary with a solid silica rod of the same outer dimension [1

1. Anders Bjarklev, Jes Broeng, and Araceli Bjarklev, Photonic Crystal Fibres, (London: Kluwer Academic Press, 2003). [CrossRef]

]. This PCF is characterized by two parameters, i.e., the hole-spacing or pitch Λ and the relative hole-size d/Λ. For a small relative hole diameter, i.e., d/Λ<0.45, such a fiber support a single mode for any wavelength [2

2. T.A. Birks, J.C. Knight, and P.St.J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997). [CrossRef] [PubMed]

], independent of the value of Λ. This allows for the development of single mode fibers with mode field diameters designable from 5 to 35 µm [3], which are useful for a number of applications including single mode power delivery. With large d/Λs and small Λs (e.g., in the range of 1–3µm), the PCFs can be made to have very small mode field area and with anomalous dispersion in visible & near infra-red regions [36

6. K. Hansen, J. Folkenberg, A. Petersson, and A. Bjarklev, “Properties of nonlinear photonic crystal fibers for telecommunication applications,” OFC 2003, 694–696 (2003).

]. These fibers are called nonlinear PCFs (NL-PCFs) that have very high effective nonlinearity and have been used for super-continuum generation. Similar small core PCFs have also been used for evanescent wave devices and sensor applications [7

7. T. Monro, D.J. Richardson, and P.J. Bennett, “Developing holey fibres for evanescent field devices,” Electron. Lett. 35, 1188–1189 (1999). [CrossRef]

, 8

8. Y. L. Hoo, W. Jin, Chunzheng Shi, Hoi L. Ho, Dong N. Wang, and Shuang C. Ruan, “Design and Modeling of a Photonic Crystal Fiber Gas Sensor,” Appl. Opt. 42, 3509–3515 (2003). [CrossRef] [PubMed]

].

In this paper, we report our findings that the PCFs with intermediate d/Λs support twomodes over extremely broad wavelength ranges and discuss the possible applications of such PCFs.

2. Two-mode PCF

Fig. 1. (a) Cross-section of a PCF with triangular lattice; (b) Λ/λc-d/Λ plot showing the two-mode operation range.

As shown in Fig. 1(b), the PCF supports only the fundamental mode below cut-off line of the second order modes, and is endlessly single mode for d/Λ<0.45. Within the shaded-region in between the cut-off lines of the second and the third order modes, the PCF supports both the fundamental mode and the second-order hybrid mode comprising of four true modes as shown in Fig. 2(b). These four true modes resemble the TE01, TM01 and the two HE21 modes in a conventional step index fiber. The two-mode region shown in Fig. 1(b) corresponds to d/Λ from approximately 0.45 to 0.65. Within this range of d/Λ, the PCF supports only the fundamental and the second-order modes for wavelength satisfying λ<λc, where λc is the cutoff wavelength of the PCF, i.e., the cut-off line of the second order modes as shown in Fig. 1b. This two-mode property holds in principle for any value of Λ, as long as the d/Λ is within the specified range as shown in Fig. 1(b). Take d/Λ=0.55 as an example, the fiber supports two hybrid modes for Λ/λ>Λ/λc≈1.6. This corresponds a two-mode wavelength range of λ<λc with λc approximately equals to 1.9µm and 3.3µm for Λ=3µm and 5µm, respectively. These wavelength ranges are practically infinite for silica fibers as they are usually not used for light transmission at wavelength beyond 1.8 µm due to the very large attenuation loss of silica material. These PCFs may then be regarded as “endlessly two-mode”, i.e., fibers that support two modes for any wavelength within the low loss window of the silica material.

Figure 2 shows the mode field patterns of the first and the second order modes for a PCF with Λ=5µm and d/Λ=0.6, at wavelength 1550nm. For the same set of parameters, the beat lengths between the fundamental and the four second order modes, defined as the lengths of fiber over which the phase difference between the respective modes changes by 2π, as functions of wavelength are shown in Fig. 3. The four curves in Fig. 3 are almost identical, indicating the approximately degenerate nature of the four second order modes.

Fig. 2. Field patterns of (a) the two polarizations of the fundamental mode; (b) the four approximately degenerate second-order modes
Fig. 3. Beat lengths between the fundamental mode and the four second-order modes as functions of wavelength.

3. Highly birefringent two-mode PCF

As discussed in Section 2, the four second-order modes are actually not exactly degenerate and the hybrid mode field intensity pattern actually varies along the fiber length due to the coherent mixing of the four modes and is not stable against environmental disturbance. The same applies to the polarization states of the fundamental mode. One way to overcome this problem is to intentionally introduce birefringence by for example having air-holes with different diameters along the two orthogonal directions [15

15. A. Ortigosa-Blanch, J.C. Knight, W.J. Wadsworth, J. Arriaga, B.J. Mangan, T.A. Birks, and P.St.J. Russell, “Highly biregringent photonic crystal fibers,” Opt. Lett. 25, 1325–1327 (2000). [CrossRef]

, 16

16. K. Suzuki, H. Kubota, S. Kawanishi, M. Tanaka, and M. Fujita, “High-speed bi-directional polarization division multiplexed optical transmission in ultra low-loss (1.3dB/km) polarization-maintaining photonic crystal fiber,” Electron. Lett. 37, 1399–1401, (2001). [CrossRef]

]. Figure 4 shows a particular PCF in which the pair of holes on the opposite sizes of the core is made bigger than the rest of the holes. This fiber is birefringent and the four second-order modes are in general non-degenerate.

Fig. 4. Cross-section of a Hi-Bi PCF

It has been reported that disorder in the air-holes leads to deformation of the higher order modes in small-core PCFs [17

17. N. A. Mortensen, M. D. Nielsen, J. R. Folkenberg, K. P. Hansen, and J. Lǽgsgaard, “Small-core photonic crystal fibers with weakly disordered air-hole cladding,” J. Opt. A: Pure Appl.Opt. 6, 221–223, 2004. [CrossRef]

]. The second-order modes split into two groups, resemble the LP11(even) and LP11(odd) hybrid modes in elliptical core fibers [18

18. B.Y. Kim, J.N. Blake, S.Y. Huang, and H.J. Shaw, “Use of highly elliptical core fibers for two-mode fiber devices,” Opt. Lett. 12, 729–731 (1987). [CrossRef] [PubMed]

] and other asymmetric waveguides [19

19. A. W. Snyder and X.-H. Zheng, “Optical fibers of arbitrary cross-sections,” J. Opt. Soc. Am. A 3, 600–609, 1986. [CrossRef]

]. The difference between the cutoff wavelengths of the two groups in small-core PCFs have been investigated experimentally and found to be as big as 42nm [14

14. J. R. Folkenberg, N. A. Mortensen, K. P. Hansen, T. P. Hansen, H. R. Simonsen, and C. Jakobsen, “Experimental investigation of cut-off phenomena in nonlinear photonic crystal fibers,” Opt. Lett. 28, 1882–2884, (2003). [CrossRef] [PubMed]

]. For the PCF shown in Fig. 4, we found that when the two bigger holes are sufficiently large, the cutoff wavelengths between the two groups can be several hundreds of nanometers [20

20. J. Ju, W. Jin, and M. S. Demokan, “Two-mode operation in highly birefringent photonic crystal fiber,” IEEE Photon. Technol. Lett. 16, 2471–2474 (2004). [CrossRef]

]. The remaining second-order modes have stable mode field pattern and polarization directions, which resemble the two orthogonal polarizations of the LP11(even) mode as in the elliptical core fibers [18

18. B.Y. Kim, J.N. Blake, S.Y. Huang, and H.J. Shaw, “Use of highly elliptical core fibers for two-mode fiber devices,” Opt. Lett. 12, 729–731 (1987). [CrossRef] [PubMed]

].

Figure 5 shows the field patterns of the fundamental and the second-order modes for a highly birefringent PCF with d/Λ=0.54, dbig/Λ=0.98 and Λ=6µm at wavelength 1550nm. Our theoretical modeling based on the intersections of the dispersion curves of waveguide modes and the fundamental space filling mode of the cladding [11

11. H. Kubota, S. Kawanishi, S. Koyanagi, M. Tanaka, and S. Yamaguchi, “Absolutely single polarization photonic crystal fiber,” IEEE Photon. Technol. Lett. 16, 182–184 (2004). [CrossRef]

], and on the observation of the mode field distributions shows that the fiber supports and only supports the fundamental LP01 and the second order LP11(even) modes within wavelength range of 0.6µm to 2µm, which covers almost the entire low loss window of the silica fibers.

Fig. 5. mode field patterns of the fundamental LP01 and the second-order LP11(even) modes.
Fig. 6. Mode indexes of the fundamental and the 2nd order modes as functions of wavelength
Fig. 7. Confinement losses of the second-order LP11(even) and LP11(odd) modes as functions of wavelength. (a) Two types of PCFs with 6 rings of air-holes; the parameters of the fibers are respectively Λ=4.18µm, d/Λ=0.54, dbig/Λ=0.97 and Λ=6µm, d/Λ=0.54, dbig/Λ=0.98. (b) The two-mode fiber designed for operation from 0.6µm to 1.8µm with 10 rings of air-holes and with Λ=6µm, d/Λ=0.54, dbig/Λ=0.98.

The computed mode indexes of the orthogonal polarizations of the two modes as functions of wavelength are shown in Fig. 6. The computed confinement losses of the LP11(even) and LP11(odd) modes, for claddings consisting of 6 and 10 rings of air-holes, as functions of wavelength are shown in Figs. 7(a) and 7(b) respectively. With 10 rings of air-holes, the confinement losses of the LP11(even) modes are less than 0.025dB/m for wavelength below 1.8µm, sufficient low for many devices applications. The LP11(odd) modes are found leaky with losses of bigger than 17dB/m for wavelength at 0.8µm and beyond. The confinement losses of the LP11(even) and LP11(odd) modes for an idealized model of a real PCF from Blazephotonics, which was designed as a single mode polarization maintaining fiber at 1.55µm, were also computed and shown in Fig. 7(a). The fiber has 6 rings of air-holes with idealized fiber parameters of Λ=4.18µm, d/Λ=0.54, dbig/Λ=0.97 [3]. This fiber was found to guide two modes (LP01 and LP11(even)) within wavelength range from ~0.65 to ~1.32µm. The measured loss of the LP11(even) mode for the two orthogonal polarization states of the Blazephotonics fiber are also shown in Fig. 7(a). The measured losses are actually smaller than those of computed ones due to discrepancies between the real fiber structure and the idealized model, as have been observed for other PCFs [21

21. M. Koshiba and K. Saitoh, “Polarization-dependent confinement losses in actual holey fibers,” IEEE Photon. Technol. Lett. 15, 691–693, 2003. [CrossRef]

]. The LP11(odd) mode was not observed within wavelength range ~0.65 to ~1.3µm even when the launching condition was varied, indicating that the PCF does not support this mode over this wavelength range.

4. Potential application

Similar to the conventional and elliptical core two-mode fibers, the two-mode PCFs discussed above can be used for a number of applications [18

18. B.Y. Kim, J.N. Blake, S.Y. Huang, and H.J. Shaw, “Use of highly elliptical core fibers for two-mode fiber devices,” Opt. Lett. 12, 729–731 (1987). [CrossRef] [PubMed]

, 22

22. J. N. Blake, B. Y. Kim, and H. J. Shaw, “Fiber-optic modal coupler using periodic microbending,” Opt. Lett. 11, 177–179 (1986). [CrossRef] [PubMed]

31

31. S. Ramachandran, “Novel photonic devices in few mode fibers,” Proc. 3rd International Conference on Optical Communications and Networks, 73–76, 30 Nov.–1 Dec. 2004.

] such as mode converters, mode selective couplers, bandpass/bandstop filters, acousto-optic frequency shifters, acoustic-optic tunable filters, wavelength tunable optical switches, add-drop multiplexers, nonlinear frequency conversion, dispersion compensator, variable optical attenuator, and interferometric fiber sensors. However, the wavelength range for two-mode operation in the PCFs is many times bigger than that of the conventional core elliptical fibers, allowing for two-mode devices with much broader wavelength range to be created. The wavelength range for two-mode operation in an elliptical core is typically limited to around 150nm [29

29. S.Y. Huang, J.N. Blake, and B.Y. Kim, “Perturbation effects on mode propagation in highly elliptical core two-mode fibers,” J. Lightwave Technol. 8, 23–33 (1990). [CrossRef]

], which sets a limit to the operating wavelength range of the two-mode devices using a particular two-mode fiber. To develop two-mode devices suitable for different operating wavelength, elliptical core fibers with different structural parameters need to be used. This requires complicated fiber design and fabrication process. Two-mode devices with different operating wavelength range may be made by using the same two-mode PCF, without going through the re-designing process. The two-mode PCFs, coupled with the use of endlessly single mode PCFs or endlessly single mode polarization maintaining PCFs as lead-in/lead-out fibers, would allow for extremely broadband devices that can not be created with conventional technologies. The dimension (e.g., Λ) of the two-mode PCF can also be scaled up and down in order to optimizing coupling to various pigtail fibers while still keeping working in the two-mode regime.

Two-mode PCF-based inteferometric strain sensors have been experimental demonstrated at wavelengths from 650nm to 1300nm [20

20. J. Ju, W. Jin, and M. S. Demokan, “Two-mode operation in highly birefringent photonic crystal fiber,” IEEE Photon. Technol. Lett. 16, 2471–2474 (2004). [CrossRef]

]. Efficient couplings from the fundamental mode to the second-order modes and to the anti-symmetric cladding modes in index-guiding PCFs have been demonstrated by periodic axial deformation [32

32. M. D. Nielsen, G. Vienne, J. R. Folkenberg, and A. Bjarklev, “Investigation of microdeformation-induced attenuation spectra in a photonic crystal fiber,” Opt. Lett. 28, 236–238, 2003. [CrossRef] [PubMed]

] and by flexural acoustic waves [33

33. A. Diez, T. A. Birks, W. H. Reeves, B. J. Mangan, and P. St. J. Russell, “Excitation of cladding modes in photonic cruystal fibers by flexural acoustic waves,” Opt. Lett. 25, 1499–1501, 2000. [CrossRef]

], respectively. These demonstrations, coupled with the availability of various two-mode fiber over practically infinite wavelength range, will allow extremely broadband devices to be developed.

5. Conclusion

Index-guiding PCFs with appropriate structural parameters were found to support the fundamental and second order modes over a practically infinite wavelength range. Highly birefringent index guiding PCFs with different size air-holes along orthogonal directions support only the LP01 and LP11(even) modes with stable mode field intensity patterns and polarization principal axes. These two-mode PCFs will have important applications in all fiber devices such as an all fiber optical filter that can be tuned from 600nm to 1800nm.

Acknowledgments

The research work was partly supported by the Hong Kong SAR Government through a CERG grant PolyU 5207/03E.

References and links

1.

Anders Bjarklev, Jes Broeng, and Araceli Bjarklev, Photonic Crystal Fibres, (London: Kluwer Academic Press, 2003). [CrossRef]

2.

T.A. Birks, J.C. Knight, and P.St.J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997). [CrossRef] [PubMed]

3.

www.crystalfiber.com and www.blazephotonics.com

4.

J.C. Knight, J. Arriaga, T.A. Birks, A. Ortigosa-Blanch, W. J. wadsworth, and P. St. J. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photon. Technol. Lett. 12, 807–809 (2000). [CrossRef]

5.

J. K. Ranka, R. S. Windeler, and A. J. Stenz, “Optical properties of high-delta air-silica microstructure optical fibers,” Opt. Lett. 25, 796–798 (2000). [CrossRef]

6.

K. Hansen, J. Folkenberg, A. Petersson, and A. Bjarklev, “Properties of nonlinear photonic crystal fibers for telecommunication applications,” OFC 2003, 694–696 (2003).

7.

T. Monro, D.J. Richardson, and P.J. Bennett, “Developing holey fibres for evanescent field devices,” Electron. Lett. 35, 1188–1189 (1999). [CrossRef]

8.

Y. L. Hoo, W. Jin, Chunzheng Shi, Hoi L. Ho, Dong N. Wang, and Shuang C. Ruan, “Design and Modeling of a Photonic Crystal Fiber Gas Sensor,” Appl. Opt. 42, 3509–3515 (2003). [CrossRef] [PubMed]

9.

W. Zhi, R. Guobin, L. Shuqin, L. Weijun, and S. Guo, “Compact supercell method based on opposite parity for Bragg fibers,” Opt. Express 11, 3542–3549 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-26-3542. [CrossRef] [PubMed]

10.

M. J. Steel and R. M. Osgood Jr, “Polarization and dispersive properties of elliptical-hole photonic crystal fibers,”J. Lightwave Technol. 19, 495–503(2001). [CrossRef]

11.

H. Kubota, S. Kawanishi, S. Koyanagi, M. Tanaka, and S. Yamaguchi, “Absolutely single polarization photonic crystal fiber,” IEEE Photon. Technol. Lett. 16, 182–184 (2004). [CrossRef]

12.

B. T. Kuhlmey, “Modal cut-off in micro-structured optical fibres,” Opt. Lett. 27, 1684–1687 (2002). [CrossRef]

13.

N. A. Mortensen, J. R. Folkenberg, M. D. Nielsen, and K. P. Hansen, “Modal cutoff and the V-parameter in photonic crystal fiber,” Opt. Lett. 28, 1879–1881, (2003). [CrossRef] [PubMed]

14.

J. R. Folkenberg, N. A. Mortensen, K. P. Hansen, T. P. Hansen, H. R. Simonsen, and C. Jakobsen, “Experimental investigation of cut-off phenomena in nonlinear photonic crystal fibers,” Opt. Lett. 28, 1882–2884, (2003). [CrossRef] [PubMed]

15.

A. Ortigosa-Blanch, J.C. Knight, W.J. Wadsworth, J. Arriaga, B.J. Mangan, T.A. Birks, and P.St.J. Russell, “Highly biregringent photonic crystal fibers,” Opt. Lett. 25, 1325–1327 (2000). [CrossRef]

16.

K. Suzuki, H. Kubota, S. Kawanishi, M. Tanaka, and M. Fujita, “High-speed bi-directional polarization division multiplexed optical transmission in ultra low-loss (1.3dB/km) polarization-maintaining photonic crystal fiber,” Electron. Lett. 37, 1399–1401, (2001). [CrossRef]

17.

N. A. Mortensen, M. D. Nielsen, J. R. Folkenberg, K. P. Hansen, and J. Lǽgsgaard, “Small-core photonic crystal fibers with weakly disordered air-hole cladding,” J. Opt. A: Pure Appl.Opt. 6, 221–223, 2004. [CrossRef]

18.

B.Y. Kim, J.N. Blake, S.Y. Huang, and H.J. Shaw, “Use of highly elliptical core fibers for two-mode fiber devices,” Opt. Lett. 12, 729–731 (1987). [CrossRef] [PubMed]

19.

A. W. Snyder and X.-H. Zheng, “Optical fibers of arbitrary cross-sections,” J. Opt. Soc. Am. A 3, 600–609, 1986. [CrossRef]

20.

J. Ju, W. Jin, and M. S. Demokan, “Two-mode operation in highly birefringent photonic crystal fiber,” IEEE Photon. Technol. Lett. 16, 2471–2474 (2004). [CrossRef]

21.

M. Koshiba and K. Saitoh, “Polarization-dependent confinement losses in actual holey fibers,” IEEE Photon. Technol. Lett. 15, 691–693, 2003. [CrossRef]

22.

J. N. Blake, B. Y. Kim, and H. J. Shaw, “Fiber-optic modal coupler using periodic microbending,” Opt. Lett. 11, 177–179 (1986). [CrossRef] [PubMed]

23.

W. V. Sorin, B. Y. Kim, and H. J. Shaw, “Highly selective evanescent modal filter for two-mode optical fibers,” Opt. Lett. 11, 581–583 (1986). [CrossRef] [PubMed]

24.

B. Y. Kim, J. N. Blake, H. E. Engan, and H. J. Shaw, “All-fiber acousto-optic frequency shifter,” Opt. Lett. 11, 389–391 (1986). [CrossRef] [PubMed]

25.

A.M. Vengsarkar, W.C. Michie, L. Jankovic, B. Culshaw, and R.O. Claus, “Fiber-optic dual-temperature sensor for simultaneous measurement of strain and temperature,” J. Lightwave Technol. 12, 170–177 (1994). [CrossRef]

26.

S. H. Yun, I. K. Hwang, and B. Y. Kim, “All-fiber tunable and laser based on two-mode fiber,”, Opt. Lett. 21, 27–29 (1996). [CrossRef] [PubMed]

27.

H. S. Park, K. Y. Song, S. H. Yun, and B. Y. Kim, All-fiber wavelength-tunable acoustooptic switches based on intermodal coupling in fibers,” J. Lightwave Technol. 20, 1864–1868 (2002). [CrossRef]

28.

J.N. Blake, S.Y. Huang, B.Y. Kim, and H.J. Shaw, “Strain effects on highly elliptical core two-mode fibers,” Opt. Lett. 12, 732–734 (1987). [CrossRef] [PubMed]

29.

S.Y. Huang, J.N. Blake, and B.Y. Kim, “Perturbation effects on mode propagation in highly elliptical core two-mode fibers,” J. Lightwave Technol. 8, 23–33 (1990). [CrossRef]

30.

L. Provino, J. M. Dudley, H. Maillotte, N. Grossard, R. S. Windeler, and B. J. Eggleton, “Compact broadband continuum source based on microchip laser pumped microstructured fiber,” Electron. Lett. 37, 558–560, 2001. [CrossRef]

31.

S. Ramachandran, “Novel photonic devices in few mode fibers,” Proc. 3rd International Conference on Optical Communications and Networks, 73–76, 30 Nov.–1 Dec. 2004.

32.

M. D. Nielsen, G. Vienne, J. R. Folkenberg, and A. Bjarklev, “Investigation of microdeformation-induced attenuation spectra in a photonic crystal fiber,” Opt. Lett. 28, 236–238, 2003. [CrossRef] [PubMed]

33.

A. Diez, T. A. Birks, W. H. Reeves, B. J. Mangan, and P. St. J. Russell, “Excitation of cladding modes in photonic cruystal fibers by flexural acoustic waves,” Opt. Lett. 25, 1499–1501, 2000. [CrossRef]

OCIS Codes
(060.2270) Fiber optics and optical communications : Fiber characterization
(060.2280) Fiber optics and optical communications : Fiber design and fabrication
(060.2340) Fiber optics and optical communications : Fiber optics components
(060.2370) Fiber optics and optical communications : Fiber optics sensors

ToC Category:
Research Papers

History
Original Manuscript: March 2, 2005
Revised Manuscript: March 9, 2005
Published: March 21, 2005

Citation
Wei Jin, Zhi Wang, and Jian Ju, "Two-mode photonic crystal fibers," Opt. Express 13, 2082-2088 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-6-2082


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References

  1. Anders Bjarklev, Jes Broeng, Araceli Bjarklev, Photonic Crystal Fibres, (London: Kluwer Academic Press, 2003) [CrossRef]
  2. T. A. Birks, J.C. Knight, and P.St.J. Russell, �??Endlessly single-mode photonic crystal fiber,�?? Opt. Lett. 22, 961-963 (1997) [CrossRef] [PubMed]
  3. <a href="http://www.crystal-fibre.com/start_page/index.shtm"> http://www.crystal-fibre.com/start_page/index.shtm</a>.
  4. J.C. Knight, J. Arriaga, T.A. Birks, A. Ortigosa-Blanch, W. J. wadsworth, and P. St. J. Russell, �??Anomalous dispersion in photonic crystal fiber,�?? IEEE Photon. Technol. Lett. 12, 807-809 (2000) [CrossRef]
  5. J. K. Ranka, R. S. Windeler, and A. J. Stenz, �??Optical properties of high-delta air-silica microstructure optical fibers,�?? Opt. Lett. 25, 796-798 (2000) [CrossRef]
  6. K. Hansen, J. Folkenberg, A. Petersson, A. Bjarklev, �??Properties of nonlinear photonic crystal fibers for telecommunication applications,�?? OFC 2003, 694-696 (2003).
  7. T. Monro, D.J. Richardson, P.J. Bennett, �??Developing holey fibres for evanescent field devices,�?? Electron. Lett. 35, 1188-1189 (1999) [CrossRef]
  8. Y. L. Hoo, W. Jin, Chunzheng Shi, Hoi L. Ho, Dong N. Wang, Shuang C. Ruan, �??Design and Modeling of a Photonic Crystal Fiber Gas Sensor,�?? Appl. Opt. 42, 3509-3515 (2003) [CrossRef] [PubMed]
  9. W. Zhi, R. Guobin, L. Shuqin, L. Weijun, and S. Guo, "Compact supercell method based on opposite parity for Bragg fibers," Opt. Express 11, 3542-3549 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-26-3542">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-26-3542</a> [CrossRef] [PubMed]
  10. M. J. Steel, R. M. Jr Osgood, �??Polarization and dispersive properties of elliptical-hole photonic crystal fibers,�?? J. Lightwave Technol. 19, 495�?? 503(2001) [CrossRef]
  11. H. Kubota, S. Kawanishi, S. Koyanagi, M. Tanaka, S. Yamaguchi, �??Absolutely single polarization photonic crystal fiber,�?? IEEE Photon. Technol. Lett. 16, 182�??184 (2004). [CrossRef]
  12. B. T. Kuhlmey, �??Modal cut-off in micro-structured optical fibres,�?? Opt. Lett. 27, 1684-1687 (2002) [CrossRef]
  13. N. A. Mortensen, J. R. Folkenberg, M. D. Nielsen, K. P.Hansen, "Modal cutoff and the V-parameter in photonic crystal fiber,�?? Opt. Lett. 28, 1879-1881, (2003) [CrossRef] [PubMed]
  14. J. R. Folkenberg, N. A. Mortensen, K. P. Hansen, T. P. Hansen, H. R. Simonsen and C. Jakobsen, �??Experimental investigation of cut-off phenomena in nonlinear photonic crystal fibers,�?? Opt. Lett. 28, 1882-2884, (2003) [CrossRef] [PubMed]
  15. A. Ortigosa-Blanch, J.C. Knight, W.J. Wadsworth, J. Arriaga, B.J. Mangan, T.A. Birks, and P. St. J. Russell, �??Highly biregringent photonic crystal fibers,�?? Opt. Lett. 25, 1325-1327 (2000) [CrossRef]
  16. K. Suzuki, H. Kubota, S. Kawanishi, M. Tanaka, and M. Fujita, �??High-speed bi-directional polarization division multiplexed optical transmission in ultra low-loss (1.3dB/km) polarization-maintaining photonic crystal fiber,�?? Electron. Lett. 37, 1399-1401, (2001) [CrossRef]
  17. N. A. Mortensen, M. D. Nielsen, J. R. Folkenberg, K. P. Hansen and J. Lǽgsgaard, �??Small-core photonic crystal fibers with weakly disordered air-hole cladding,�?? J. Opt. A: Pure Appl.Opt. 6, 221-223, 2004. [CrossRef]
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